2017/06/13 by Cory Palmer, Palmer, Cory, Michael Tait +5 · 1 citation
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Limits and Structures in Graph Theory
paper · pdf · doi:10.48550/arxiv.1706.04249
openalex publication_date 2017/06/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let F be a graph. We say that a hypergraph H is a it Berge-F if\nthere is a bijection f : E(F) \→ E(H ) such that e \⊆ f(e)\nfor every e \∈ E(F). Note that Berge-F actually denotes a class of\nhypergraphs. The maximum number of edges in an n-vertex r-graph with no\nsubhypergraph isomorphic to any Berge-F is denoted\n exr(n, textrmBerge-F). In this paper we establish new upper and lower\nbounds on exr(n, textrmBerge-F) for general graphs F, and investigate\nconnections between exr(n, textrmBerge-F) and other recently studied\nextremal functions for graphs and hypergraphs. One case of specific interest\nwill be when F = Ks,t. Additionally, we prove a counting result for\nr-graphs of girth five that complements the asymptotic formula textupex3\n(n , textrmBerge- C2 , C3 , C4 ) = \(1)/(6) n3/2 + o( n3/2\n) of Lazebnik and Verstra "ete [ em Electron. J. of Combin. bf 10,\n(2003)].\n